where \(\vec{u}\) 
is a learnable weight vector,
\(\vec{\psi }_A(a), \vec{\psi }_W(w)\)  are vectors of fixed basis functions, and \(\otimes \)  is a Kronecker product, defined as \(\vec{a} \otimes \vec{b} = \mathrm {vec}(\vec{a}\vec{b}^\top )\)  for any finite dimensional vectors \(\vec{a}, \vec{b}\) .Throughout this paper, we assume the number of basis functions to be finite. Mastouri and Zhu et al. [1]}considers an infinite number of basis function in a reproducing kernel Hilbert space, in which they use the definition of the inner product and Kronecker product for that space.
An estimate \(\hat{\vec{u}}\)  is obtained by solving the successive regression problems. In Stage 1, we estimate the conditional expectation \([W|A=a,Z=z]{\vec{\psi }_W(W)}\)  as a function of \(a,z\) .
In Stage 2, we substitute the model
(REF ) into the inner conditional expectation in \(\mathcal {L}_{\mathrm {PV}}\)
\([W|A=a,Z=z]{h(a,W)} = \vec{u}^\top (\vec{\psi }_A(a) \otimes [W|A=a,Z=z]{\vec{\psi }_W(W)}),\) 
